What was the mistake made in solving this equation:

6(2y+6)=4(9+3y)

12y+36=36+12y

12y=12y

This equation has no solution

If you subtracted 36 from both sides why not subtract 12 y from both sides and get

0 = 0
That is not a mistake, it is true. Any old value of y is a solution :) Go back and try y = 597.1328

The mistake made in solving this equation is that both sides of the equation were divided by 12y. This led to the equation 12y = 12y, which means that the variable y cancels out on both sides. As a result, there are no variables left in the equation to solve for, and therefore, there is no solution.